Journal of Inverse and Ill-posed Problems
Editor-in-Chief: Kabanikhin, Sergey I.
6 Issues per year
IMPACT FACTOR increased in 2015: 0.987
Rank 59 out of 312 in category Mathematics and 93 out of 254 in Applied Mathematics in the 2015 Thomson Reuters Journal Citation Report/Science Edition
SCImago Journal Rank (SJR) 2015: 0.583
Source Normalized Impact per Paper (SNIP) 2015: 1.106
Impact per Publication (IPP) 2015: 0.712
Mathematical Citation Quotient (MCQ) 2015: 0.43
Use of extrapolation in regularization methods
Extrapolation is a well-known tool for increasing the accuracy of approximation methods. We consider extrapolation of Tikhonov and Lavrentiev methods and iterated variants of these methods for solving linear ill-posed problems in Hilbert space. For extrapolated approximation we take the linear combination of n ≥ 2 approximations of the original method with different parameters and with proper coefficients, guaranteeing for extrapolated method higher qualification than in original method. Extrapolated approximation can be used for approximation to solution of the equation or for construction of a posteriori rules for choice of the regularization parameter in original method. As shown, extrapolating n Tikhonov or Lavrentiev approximations gives the same approximation as one gets in nonstationary implicit iterative method after n iterations with the same parameters. If the solution is smooth and δ is noise level of data, a proper choice of n = n(δ) guarantees for extrapolated Tikhonov approximation accuracy versus accuracy of Tikhonov approximation. Note that in a posteriori parameter choice in Tikhonov method often several approximations with different parameters are computed and then computation of their linear combination is an easy task.
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